Question

Shown below is a distribution of charges. The flux of electric field due to these charges through the surface $S$ is

• A. $\frac{3q}{{\epsilon }_0}$
• B. $\frac{2q}{{\epsilon }_0}$
• C. $\frac{q}{{\epsilon }_0}$
• D. zero

Answer 1

Answer: (D)

According to Gauss's theorem, the electric flux through any closed surface is equal to $1/{\epsilon }_0$ times the net charge $q$ enclosed by the surface, that is
${\varphi }_E=\oint \vec{E}\cdot d\vec{A}=\frac{q}{{\epsilon }_0}$
Since total charge enclosed by surface is zero,
$\therefore$ Total electric flux, $\varphi =0$